Synthesis of modal control of multidimensional crystallization process by van der woude

Abstract

Using the systems of non-adaptive control, in particular, modal for high-quality control over linear dynamic objects is discussed and some results of our research in this area are given in the paper.The primary objective of the study is to solve the problem of modal control synthesis for a multidimensional object based on the Van der Woyd’s generalized approach, as well as on using the knowledge in the field of control, obtained from different sources, for the process of growing single crystals using the Czochralski method on the “GROWTH”-type setups. Using modern methods and tools for analyzing the properties of linear controllable systems leads to the need of using modal controllability of the system and solving the problem of synthesis of modal control over the multidimensional object.In the paper, generalization of the Van der Woyd’s theorem in terms of band matrices for the case of MIMO-system modal control is given in the form of the algorithm, difference vectors of coefficients of specified and initial characteristic polynomials with respect to the growing process as the control object are described and parameterized. Using the graphical representation of the transfer characteristics of the object and closed-loop system in trajectory areas for analysis allows to obtain important information about the high-quality system control.It is proposed to use this method for increasing the dynamic quality of control over inertial objects, which is the process of growing crystals in order to increase the efficiency of control systems for modern growth setups in conditions of producing these crystals.The research results can be applied by specialists in the field of modal control over material, energy and information flows in control systems for modern technological processes, integrated into the technical environment of these processes